Quantum metrology

Can a fully general adaptive strategy attain a larger Stein exponent than every nested-adaptive strategy for discriminating two quantum superchannels?

• Quantum metrology
• Channel discrimination
• Quantum hypothesis testing
• Superchannels and quantum combs

Does amortization collapse for the max-relative entropy and geometric Rényi divergence of arbitrary finite-dimensional quantum superchannels?

• Quantum metrology
• Quantum Communication
• Channel discrimination
• Quantum relative entropy
• Superchannels and quantum combs

Can nested-adaptive strategies improve the Stein exponent for discriminating two finite-dimensional quantum superchannels?

• Quantum metrology
• Channel discrimination
• Quantum hypothesis testing
• Superchannels and quantum combs

Does the Ježek–Řeháček–Fiurášek (JRF) iteration, initialized by the uniform POVM, converge to a globally optimal minimum-error measurement for every finite ensemble containing mixed quantum states?

• Quantum metrology
• Quantum state discrimination

Does quantum control of causal order yield a persistent asymptotic metrological advantage over parallel access for some smooth finite-dimensional channel family?

• Quantum metrology
• Quantum Resource Theory
• Quantum estimation
• Indefinite causal order

Let \(\mathcal N,\mathcal M:\mathcal L(A)\to\mathcal L(B)\) be quantum channels on finite-dimensional systems.

• Quantum metrology
• Quantum Communication
• Channel discrimination
• Quantum hypothesis testing
• Quantum relative entropy
• Strong converses

Let \(\mathcal N:\mathcal L(A)\to\mathcal L(B)\) be a finite-dimensional quantum channel.

• Quantum Resource Theory
• Quantum metrology
• Quantum hypothesis testing
• Channel discrimination
• Quantum relative entropy

Does a symmetric informationally complete positive-operator-valued measure exist in every finite dimension \(d\ge2\)?

• Quantum metrology
• Symmetric informationally complete measurements

Does every finite dimension admit a symmetric informationally complete measurement that is a single Weyl–Heisenberg orbit?

• Quantum metrology
• Symmetric informationally complete measurements

For every \(d\geq3\), do the standard CGLMP Fourier–phase measurements maximize the relative-entropy statistical strength against local realism among all projective \(d\)-outcome measurements on the fixed state \(\lvert\Phi_d\rangle=d^{-1/2}\sum_{j=0}^{d-1}\lvert j,j\rangle\), when the setting distribution is also optimized?

• Quantum Resource Theory
• Quantum metrology
• Bell nonlocality
• Quantum hypothesis testing

For each integer \(d\geq2\), determine the maximum number \(\mu(d)\) of pairwise mutually unbiased orthonormal bases of \(\mathbb C^d\).

• Quantum metrology
• Mutually unbiased bases

For every \(d\geq3\), do the standard Fourier–phase measurements optimize the CGLMP violation of the maximally entangled state among all projective \(d\)-outcome measurements?

• Quantum Resource Theory
• Quantum metrology
• Bell nonlocality

Does every finite dimension admit a Weyl–Heisenberg SIC fiducial that is an eigenvector of a Zauner Clifford unitary?

• Quantum metrology
• Symmetric informationally complete measurements